// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_ROTATION2D_H
#define EIGEN_ROTATION2D_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 * \class Rotation2D
 *
 * \brief Represents a rotation/orientation in a 2 dimensional space.
 *
 * \tparam _Scalar the scalar type, i.e., the type of the coefficients
 *
 * This class is equivalent to a single scalar representing a counter clock wise rotation
 * as a single angle in radian. It provides some additional features such as the automatic
 * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
 * interface to Quaternion in order to facilitate the writing of generic algorithms
 * dealing with rotations.
 *
 * \sa class Quaternion, class Transform
 */

namespace internal {

template<typename _Scalar>
struct traits<Rotation2D<_Scalar>>
{
	typedef _Scalar Scalar;
};
} // end namespace internal

template<typename _Scalar>
class Rotation2D : public RotationBase<Rotation2D<_Scalar>, 2>
{
	typedef RotationBase<Rotation2D<_Scalar>, 2> Base;

  public:
	using Base::operator*;

	enum
	{
		Dim = 2
	};
	/** the scalar type of the coefficients */
	typedef _Scalar Scalar;
	typedef Matrix<Scalar, 2, 1> Vector2;
	typedef Matrix<Scalar, 2, 2> Matrix2;

  protected:
	Scalar m_angle;

  public:
	/** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
	EIGEN_DEVICE_FUNC explicit inline Rotation2D(const Scalar& a)
		: m_angle(a)
	{
	}

	/** Default constructor wihtout initialization. The represented rotation is undefined. */
	EIGEN_DEVICE_FUNC Rotation2D() {}

	/** Construct a 2D rotation from a 2x2 rotation matrix \a mat.
	 *
	 * \sa fromRotationMatrix()
	 */
	template<typename Derived>
	EIGEN_DEVICE_FUNC explicit Rotation2D(const MatrixBase<Derived>& m)
	{
		fromRotationMatrix(m.derived());
	}

	/** \returns the rotation angle */
	EIGEN_DEVICE_FUNC inline Scalar angle() const { return m_angle; }

	/** \returns a read-write reference to the rotation angle */
	EIGEN_DEVICE_FUNC inline Scalar& angle() { return m_angle; }

	/** \returns the rotation angle in [0,2pi] */
	EIGEN_DEVICE_FUNC inline Scalar smallestPositiveAngle() const
	{
		Scalar tmp = numext::fmod(m_angle, Scalar(2 * EIGEN_PI));
		return tmp < Scalar(0) ? tmp + Scalar(2 * EIGEN_PI) : tmp;
	}

	/** \returns the rotation angle in [-pi,pi] */
	EIGEN_DEVICE_FUNC inline Scalar smallestAngle() const
	{
		Scalar tmp = numext::fmod(m_angle, Scalar(2 * EIGEN_PI));
		if (tmp > Scalar(EIGEN_PI))
			tmp -= Scalar(2 * EIGEN_PI);
		else if (tmp < -Scalar(EIGEN_PI))
			tmp += Scalar(2 * EIGEN_PI);
		return tmp;
	}

	/** \returns the inverse rotation */
	EIGEN_DEVICE_FUNC inline Rotation2D inverse() const { return Rotation2D(-m_angle); }

	/** Concatenates two rotations */
	EIGEN_DEVICE_FUNC inline Rotation2D operator*(const Rotation2D& other) const
	{
		return Rotation2D(m_angle + other.m_angle);
	}

	/** Concatenates two rotations */
	EIGEN_DEVICE_FUNC inline Rotation2D& operator*=(const Rotation2D& other)
	{
		m_angle += other.m_angle;
		return *this;
	}

	/** Applies the rotation to a 2D vector */
	EIGEN_DEVICE_FUNC Vector2 operator*(const Vector2& vec) const { return toRotationMatrix() * vec; }

	template<typename Derived>
	EIGEN_DEVICE_FUNC Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
	EIGEN_DEVICE_FUNC Matrix2 toRotationMatrix() const;

	/** Set \c *this from a 2x2 rotation matrix \a mat.
	 * In other words, this function extract the rotation angle from the rotation matrix.
	 *
	 * This method is an alias for fromRotationMatrix()
	 *
	 * \sa fromRotationMatrix()
	 */
	template<typename Derived>
	EIGEN_DEVICE_FUNC Rotation2D& operator=(const MatrixBase<Derived>& m)
	{
		return fromRotationMatrix(m.derived());
	}

	/** \returns the spherical interpolation between \c *this and \a other using
	 * parameter \a t. It is in fact equivalent to a linear interpolation.
	 */
	EIGEN_DEVICE_FUNC inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
	{
		Scalar dist = Rotation2D(other.m_angle - m_angle).smallestAngle();
		return Rotation2D(m_angle + dist * t);
	}

	/** \returns \c *this with scalar type casted to \a NewScalarType
	 *
	 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
	 * then this function smartly returns a const reference to \c *this.
	 */
	template<typename NewScalarType>
	EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Rotation2D, Rotation2D<NewScalarType>>::type cast()
		const
	{
		return typename internal::cast_return_type<Rotation2D, Rotation2D<NewScalarType>>::type(*this);
	}

	/** Copy constructor with scalar type conversion */
	template<typename OtherScalarType>
	EIGEN_DEVICE_FUNC inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
	{
		m_angle = Scalar(other.angle());
	}

	EIGEN_DEVICE_FUNC static inline Rotation2D Identity() { return Rotation2D(0); }

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	 * determined by \a prec.
	 *
	 * \sa MatrixBase::isApprox() */
	EIGEN_DEVICE_FUNC bool isApprox(
		const Rotation2D& other,
		const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
	{
		return internal::isApprox(m_angle, other.m_angle, prec);
	}
};

/** \ingroup Geometry_Module
 * single precision 2D rotation type */
typedef Rotation2D<float> Rotation2Df;
/** \ingroup Geometry_Module
 * double precision 2D rotation type */
typedef Rotation2D<double> Rotation2Dd;

/** Set \c *this from a 2x2 rotation matrix \a mat.
 * In other words, this function extract the rotation angle
 * from the rotation matrix.
 */
template<typename Scalar>
template<typename Derived>
EIGEN_DEVICE_FUNC Rotation2D<Scalar>&
Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
{
	EIGEN_USING_STD(atan2)
	EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime == 2 && Derived::ColsAtCompileTime == 2,
						YOU_MADE_A_PROGRAMMING_MISTAKE)
	m_angle = atan2(mat.coeff(1, 0), mat.coeff(0, 0));
	return *this;
}

/** Constructs and \returns an equivalent 2x2 rotation matrix.
 */
template<typename Scalar>
typename Rotation2D<Scalar>::Matrix2 EIGEN_DEVICE_FUNC
Rotation2D<Scalar>::toRotationMatrix(void) const
{
	EIGEN_USING_STD(sin)
	EIGEN_USING_STD(cos)
	Scalar sinA = sin(m_angle);
	Scalar cosA = cos(m_angle);
	return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
}

} // end namespace Eigen

#endif // EIGEN_ROTATION2D_H
